Question

Find the measure of x,y,z in the following parallelograms.​

Answer 1

Answer:

(i) x+8=16-x (because diagonal of Parallelogram bisect each other)

2x=8

x=4

5y+4=2y+13(because diagonal of Parallelogram bisect each other)

5y-2y=13-4

3y=9

y=3

(ii)3x+1=2x+3(because diagonal of Parallelogram bisect each other)

3x-2x=3-1

x=2

5y-2=4-y(because diagonal of Parallelogram bisect each other)

5y+y=4+2

6y=6

y=6/6

y=1

4z-2=2z+6(because opposite sides of Parallelogram are equal)

4z-2z=6+2

2z=8

z=8/2

z=4

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Answer 2

Answer:

Step-by-step explanation: fig i - as we know that diagonals of the parallelogram are equal:

= 5y + 4 = 2y + 13

= 5y-2y = 13-4 ( transposing 2y to left hand side and 4 to right hand side )

= 3y = 9

= y = 3

= x + 8 = 16 - x

= x+x = 16 - 8 ( transposing x to left hand side and 8 to right hand side )

= 2x = 8

= x = 4

fig ii -

as we know that diagonals of the parallelogram are equal and opposite sides are parallel to eachother.

= 5y-2 = 4 - y

= 5y + y = 4+2 ( transposing y to LHS and 2 to RHS )

= 6Y= 6

= y = 1

= 3x + 1 = 2x + 3

= 3x - 2x = 3 - 1 ( transposing 2x to LHS and 1 to RHS )

= 1X = 1

= x = 1

= 4z - 2 = 2z + 6

= 4z - 2z = 6 + 2 ( transposing 2z to LHS and 2 to RHS )

= 2z = 8

= z = 4

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